Question

4. Technology required. Two objects are launched upward. Each function gives the

distance from the ground in meters as a function of time, 1, in seconds.
Object A: f(t) = 25+20t - 5t^2
Object B: g(t) = 30 + 10t - 5t^2
Use graphing technology to graph each function.
a. Which object reaches the ground first? Explain how you know.
b. What is the maximum height of each object?

Answer 1

To graph the functions f(t) and g(t), we plot the distance from the ground on the y-axis and the time on the x-axis. We determine which object reaches the ground first by finding the time when each function equals zero. To find the maximum height of each object, we determine the vertex of each function.

To graph the functions f(t) = 25+20t - 5t^2 and g(t) = 30 + 10t - 5t^2, we plot the distance from the ground on the y-axis and the time on the x-axis.

a. To determine which object reaches the ground first, we find the time when each function equals zero. For f(t), we solve 25+20t - 5t^2 = 0. For g(t), we solve 30 + 10t - 5t^2 = 0. The object that reaches the ground first is the one that has a shorter time when the function equals zero.

b. To find the maximum height of each object, we determine the vertex of each function. The vertex represents the highest point on the graph. The y-coordinate of the vertex gives us the maximum height of the object.